Question

Турист идет из одного города в другой, каждый день проходя больше, чем в предыдущий день, на одно и то же расстояние. Известно, что за первый день турист прошел 10 километров. Определите, сколько километров прошел турист за третий день, если весь путь он прошел за 9 дней, а расстояние между городами составляет 162 километров(Сделайте рисунок или схемку или табличку

Answer 1

Ответ:

Пошаговое объяснение:

Решим методом арифметической прогрессии. Составим таблицу

a1      а3   n    d      Sn

10     ?     9    ?      162

Пусть в первый день турист прошел a1 =10 км, тогда в последний день a9 км. Всего он прошел Sn= 162 км. Если каждый день турист проходил больше, чем в предыдущий день, на одно и то же расстояние то найдем разность арифметической прогрессии d км,

S= (2an-1 + d(n-1)/2))*n =2*10+ d(9-1)/2))*9= (20+8d)/2))*9= 162

36d=72  

d= 72: 36

d= 2 км на столько больше проходил  турист каждый день

а3 = а1 + 2d = 10 + 2 * 2 = 14 км столько километров прошел турист за третий день

Answer 2

Problem Analysis

A tourist is traveling from one city to another, covering a greater distance each day compared to the previous day. The tourist covered 10 kilometers on the first day and completed the entire journey in 9 days. The distance between the cities is 162 kilometers. We need to determine how many kilometers the tourist covered on the third day.

Solution

To solve this problem, we can use the concept of arithmetic progression. In an arithmetic progression, each term is obtained by adding a constant difference to the previous term.

Let's assume that the distance covered by the tourist on the third day is x kilometers. We know that the distance covered on the first day is 10 kilometers.

The total distance covered in 9 days can be calculated using the formula for the sum of an arithmetic progression:

Sum = (n/2)(2a + (n-1)d)

Where: - Sum is the total distance covered in 9 days (162 kilometers in this case) - n is the number of terms (9 days in this case) - a is the first term (10 kilometers in this case) - d is the common difference (the difference in distance covered each day)

We can rearrange the formula to solve for d:

d = (Sum - n*a) / ((n-1)*n/2)

Substituting the given values, we can calculate the common difference d.

Once we have the common difference, we can calculate the distance covered on the third day using the formula for the nth term of an arithmetic progression:

nth term = a + (n-1)d

Substituting the values, we can calculate the distance covered on the third day.

Calculation

Let's calculate the distance covered on the third day using the given values.

Given: - First day distance (a) = 10 kilometers - Total distance covered in 9 days (Sum) = 162 kilometers - Number of terms (n) = 9 days

Using the formula for the common difference (d):

d = (Sum - n*a) / ((n-1)*n/2)

Substituting the values:

d = (162 - 9*10) / ((9-1)*9/2) = 12 kilometers

Using the formula for the nth term:

nth term = a + (n-1)d

Substituting the values:

Third day distance = 10 + (3-1)*12 = 34 kilometers

Answer

The tourist covered 34 kilometers on the third day.

Visual Representation

Here is a visual representation of the distances covered each day:

| Day | Distance (kilometers) | |-----|----------------------| | 1 | 10 | | 2 | 22 | | 3 | 34 | | 4 | 46 | | 5 | 58 | | 6 | 70 | | 7 | 82 | | 8 | 94 | | 9 | 106 |

Please let me know if you need any further assistance!